Origin point different in editmode / objectmode
As said in the comments by Serge L and Mr Zak, if you want the vertices to rotate around the origin in edit mode, you have to set the cursor to the origin (Shift+S cursor to selected, if the object is selected) and then set the cursor as pivot point, so that every rotation and scaling will use the cursor location as pivot point.

Turning on or off the manipulators is only a visual utility, which doesn't affect the rotation behaviours.

The logic behind this is the fact that the default pivot point is the median point: in object mode you have only one object selected so the median point (pivot point) is the object origin. In edit mode you select all vertices of the mesh, and the middle point will be a location which will have the average coordinates of all vertices, and this (often empty) location will act as pivot point.